Electrostatic 512kV rotator and/or oscillator propulsion system

ABSTRACT

Some recent experimental work(Pod,2001) implies that an electron cloud with external pulse from a superconductor(SC) can be generated at above approximately 500 kV. Also U.S. Pat. Nos. 593,138 and 4,661,747 imply that this can happen for nonSCs with rotating clouds of electrons above 500 kV. This can be theoretically explained simply by making General-Relativity(GR) algebraicly complete since the harmonic-coordinates are already physical (not gauge-coordinates) due to the Dirac-particle zitterbewegung oscillation. This UngaugedGR augmented by the Dirac-equation then results in the weak-field Einstein-equations being the Maxwells-equations which then imply a charge-source 8πke 2 /c 2  on the righthand side. One result of this Ungauged-GR is that you can do a radial-coordinate transformation of this E&amp;M ke 2  Einstein-equation source to the coordinate system comoving with that sin hωt cosmological expansion resulting in (a added) classical-gravitational-source that can then be cancelled by creating an artificial-coordinate-transformation. A rotating disk at just above 512 kV appears to provide this annulment and so our propulsion-patent-details.

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] Not Applicable

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

[0002] There was no Federally sponsored research or development involvedin this patent.

BACKGROUND OF THE INVENTION

[0003] It is well known that there are four more metric coefficientsthan independent Einstein equations thus making general relativity“incomplete”. The solution has been to regard the Einstein equations asa gauged theory (Weinberg, 1972). For example the harmonic “gauge” iscommonly used here in the weak field approximation givingR_(αα)≈□²h_(αα)=0≡k^(α)k_(α)=0 which imply the required four harmonicgauge (additional) equations${k_{\mu}e_{v}^{\mu}} = {\frac{1}{2}k_{v}e_{\mu}^{\mu}}$

[0004] (Weinberg, 1972). But in the zitterbewegung oscillating system ofa (Dirac equation) lepton this harmonic coordinate system is actuallyphysical, not gauged, making the Einstein equations a ‘complete’,ungauged, theory in that case. But the augmentation of the Einsteinequations by the Dirac equation introduces iterated Σk=0 empty spacesolutions to k^(α)k_(α)=0 which when Σk=0 is substituted into${\sum{k_{\mu}e_{v}^{\mu}}} = {\sum{\frac{1}{2}k_{v}e_{\mu}^{\mu}}}$

[0005] give new solutions to the Einstein equations: the Maxwellequations in the weak field limit (i.e., E&M). This implies that an E&Msource (such as Z_(oo)=8πe²/mc²δ(0))≡8πkδ(0)) could be used in theEinstein equations instead of the standard gravitational source 8πGρ.And with this E&M source in the Einstein's equations the perturbations(to the Coulomb potential) coming out of the metric solutions to thesenew Einstein equations give the Lamb shift when applied to the 2,0,0eigenfunction (so just one vertex QED, no renormalization) and the newDirac equation S matrix gives the W and Z as resonances. Again thistheory is not a gauge theory anymore (as we said) so 2k=r is in fact asingularity that cannot be gauge transformed away. Thus if the sourcesare 2k=r apart the clocks slow down, you have stability (i.e., theproton, note again that k∝e², not 8πGρ) but for r<k you have asymptoticfreedom as in QCD. Finally in the end we can do a radial coordinatetransformation (of Z_(oo)) to the coordinate system comoving with thatcosmological expansion, the new additional term that results turns outto be that standard gravitational source. In a ungauged GR it is alsopossible to limit the number of implicit assumptions by allowing forfractalness within unobservable regions, within horizons. In combiningthe set of such Dirac equations, one for each fractal scale, one gets(using separability) a physical wavefunction which is a product of thetime dependent Dirac eigenfunctions over fractal scales. The M+1 th lowfrequency Dirac eigenfunction gives nearly m=0, so a neutrinoH_(v)ψ=σ·ρ_(v)ψ. From the fractalness the outside observer sees ae^(iωt) (ω=<H>/

) or sin ωt and so because of the square root in g_(oo) as the r goesthrough k the inside observer sees a sin ωt→sin hωt. Thus the insideobserver sees exponential expansion. The sum of the Hs in this sin hωtmust be zero since t is arbitrary so H_(v) is the negative of H_(e)(electron) giving negative helicity σ·ρ_(v), thus giving a left handeddoublet (electron and neutrino) with zero and nonzero mass. We can thuscreate the core of the standard model from the fractal assumption. Alsohere we found that the universe is then expanding with r=r_(o) sin hωt.So if you do a radial coordinate transformation to the coordinate systemcomoving with the r=r_(o) sin hωt expansion you get the old Z_(oo) plusa small additional source z_(oo), the gravitational source.

BRIEF SUMMARY OF THE INVENTION

[0006] Propulsion implications arise if we can cancel out (i.e., annul)the effect of that coordinate transformation. To do this we introduce aartificially created Kerr metric structure with the above 8πe²/mc²source(not the usual Gρ): same math as Kerr metric, new source. Thisartificial (E&M) Kerr metric as a quadratic structure and we can thenfind the solution from the quadratic formula. We find a term in thedenominator of this result that is zero for a specific rotating electricfield configuration thereby making an arbitrarily large contribution. Weuse this artificial metric to cancel the effect of the z_(oo)due to thecoordinate system comoving with this expansion. In doing so we find az_(oo) annulment term C^(o)/dt has a angular momentum in the numeratorand a A=1-e2V/2 mc² in the denominator: $\begin{matrix}{\frac{C^{0}}{t} = {{c^{2}\left( {2\frac{V}{512k}} \right)}\frac{\left( {v/c} \right)r\quad \sin^{2}\theta {\theta}}{{t}\quad {c^{2}\left\lbrack {1 - {{V/512}k}} \right\rbrack}}}} & (1)\end{matrix}$

[0007] For rotating charge there is a large (repulsive) gravitationalpropulsion effect for A=0 (=1-2 eV/2 mc²) so that V=512 kV if m is theelectron mass. Also if the voltage is increased fast enough there willbe a consecutive repelling and attractive propulsive pulse released.

[0008] So the two forms of the invention are a counterrotating set ofcapacitor plates at just above 512 kV with the other one being arotating disc (with associated anode) given voltage provided by rampingup voltage through 512 kV up to 2 MV. The thrust is provided by theimpulse coming off the anode.

[0009] Electrostatic 512 kV Rotar and/or Oscillator Propulsion System

[0010] Electrostatic—Uses high voltage produced by electrostatic chargegenerator.

[0011] 512 kV—2 mc²/2 e=512,000 volts in the denominator of equation 1

[0012] Rotator—The rotation (that vr in equation 1) is provided byrotating capacitor plates or electrons in the vortices of a type IIsuperconductor.

[0013] Oscillator—If just above 512 kV we must have non zero ω=dθ/dtoscillation. For a ‘ramping’ voltage (from 0→3 MV lets say) thisoscillation is not necessary.

[0014] Propulsion System—For the ramping voltage a mg (mostly repulsive)pulse is sent out. Use Newton's 3 law to get reaction, or propulsive,force. For voltage at a just above a steady 512 kV there is nopropulsion but there is still annulment, hovering.

BRIEF DESCRIPTION OF THE FOUR DRAWINGS

[0015] FIG. A—Rotating Capacitors at just above 512 kV. Hovering.

[0016] FIG. B—Rotating Capacitors at just above 512 kV(details)

[0017] FIG. C—Ramped up voltage propulsion

DETAILED DESCRIPTION OF THE INVENTION

[0018] In this type of General Relativity (GR) the 6 independentequations (with the 10 unknown g_(ij) s) are augmented by the 4 physical(not gauged) harmonic coordinate conditions of the Dirac equationzitterbewegung oscillation thereby showing that GR is algebraiclycomplete. Augmenting the Einstein equations with the Dirac equationmakes the Einstein equations into the Maxwell equations (E&M) in theweak field limit thus implying that we should use a E&M source e²/mc²instead of the usual Gρ source on the right hand of the 0-0 component.There is a lot of evidence that this is correct. For example when youplug back into the Dirac equation the potentials you get from these newEinstein equations give you the Lamb shift without the need for higherorder Feynman diagrams or renormalization and the new single vertexDirac equation S matrix gives the W and Z as resonances. Note that weare merely noting that GR is complete anyway without adding any newassumptions.

[0019] No New Assumptions, in Fact One Less Assumption

[0020] In this section we do not implicitly assume that GR is referencedto only one particular scale. Out of the range of observability, inother words on the other side of either big or small horizons, there canbe larger or smaller horizons all over again (fractalness). So there isone less assumption, that GR is referenced to only one particular scale.We simply drop this otherwise implicitly held assumption. So there is aEinstein equation curvature scalar R on each (N th) fractal scale and aDirac equation ψ for each N th fractal scale. Here the N+1(cosmological) fractal scale is about 10⁴⁰ times larger than the N th(electron) fractal scale. Rotation is nearly unobservable for the N+1cosmological scale because of inertial frame dragging. Also we are usingthe Einstein equations so we impose general covariance on ourlagrangians on each N th fractal scale. So we can write the lagrangianimplied by the fractalness as a general covarient Dirac equation partplus an Einstein equation part summed over all fractal scales:$\begin{matrix}{L_{fractal} = {\sum\limits_{N = 1}^{\infty}\quad \left( {{{i\left( \psi^{t} \right)}{N\quad}^{\gamma}\quad {\mu \left( {{\sqrt{g_{\mu \quad \mu}}\psi},\mu} \right)}_{N}} + {m\left( \psi^{t} \right)}_{{N\quad}^{\psi}\quad N} + {\sqrt{g_{N}}R_{N}} + \left( L_{Source} \right)_{N}} \right)}} & (1)\end{matrix}$

[0021] Note that E=(dt/ds){square root}g_(oo). Again the 0-0 source forthe Nth fractal scale is 8πe²/mc² not Gρ.

[0022] Fractal Dirac Equation

[0023] The equation 1 lagrangian implies that the Dirac equation ψ s arealso fractal with a ψ_(M) for each fractal scale M. So instead of justthe single scale Dirac equation (Merzbacher, 1970):

ψ+i(1)βψ=0

[0024] we have a infinite succession of such equations:

(

ψ+i(1)βψ=0)_(M−1), (

ψ+i(1)βψ=0)_(M), (

ψ+i(1)βψ=0)_(M+1),

[0025] one for each fractal scale. Note from the lagrangian of equation1 (with the Einstein equation component) the physical regions in whicheach of these equations apply are separated by a event horizon. Thephysical effects on the ambient metric begin with the M+1 scale equationif M+1 is the scale of our own cosmological ambient metric. Also thissequence of Dirac equations is equivalent to a single separabledifferential equation in the ψ_(M) s. Thus, as in all cases ofseparability, we can write a product function of the ambient ψ_(M) s:${\prod\limits_{N = {M + 1}}^{\infty}\quad \Psi_{N}} = {{\Psi_{M + 1} \cdot \Psi_{M + 2} \cdot \ldots} = \Psi_{Physical}}$

[0026] But these Dirac eigenfunctions have the energies in theirexponents (Ψ∝e^(iωt)=e^(I<H>t/z,902) ) in general we can also write(with k a column matrix): $\begin{matrix}{\Psi_{physical} = {{k\quad {\exp \left( {{\left( {1/\hslash} \right)}{\sum\limits_{N = {M + 1}}^{\infty}\quad {H_{N}t}}} \right)}} = {k\quad {\exp \left( {{\left( {1/\hslash} \right)}H_{{{physical}\quad}^{t}}} \right)}}}} & (2)\end{matrix}$

[0027] We define the H s such that “t” here is the proper time for theobserver in the M+1 th fractal scale to make Ψ^(t)Ψ physical for the M+1th fractal scale. Also recall that Hψ=Eψ. The zitterbewegung oscillationalso will have this r=r_(o)e^(iωt) dependence. dt/ds=1/g_(oo) so in theabove Dirac equation $\begin{matrix}{{H \propto {\left( {{t}/s} \right)\left. \sqrt{}g_{oo} \right.} \propto {{1/\left. \sqrt{}g_{oo} \right.}\quad {{SO}:\quad \quad {\omega \propto H \propto {1/\sqrt{g_{00}}}}}}} = {1/\sqrt{1 - {k_{H}/r}}}} & (3)\end{matrix}$

[0028] as r gets less than k_(H) the square root becomes imaginary. So ωbecomes imaginary. So if on the outside (i.e.,r>k_(H)) Ψ∝sin ωt (andzitterbewegung then sin μ≡sin ωt→sin(iωt)=sin hωt as you go to theinside (i.e., r<k_(H)). Thus for: Ψ and (zitterbewegung r=r_(o)e^(iΨt))

Both r and Ψ_(M)∝sin hωt inside, r and ω_(M)∝sin ωt outside  (4)

[0029] So because of our observation point inside the horizon of allthese ψ_(M) s those “i” s in the exponents in equation 2 will end upgoing away as in the sin hωt of equation 4. So the universe willaccelerate in its expansion (since also r→r_(o) sin hωt). Also becauseof the large M+1 th (cosmological) scale oscillation time T (in ω≡2π/T)the Dirac eigenfunction contribution to equation 2 is:

Zitterbewgung_(M+1)=ω_(M)+1≈0 (recall m∝ω_(M+1)) so thenH_(M+1)≡σ·ρ  (5)

[0030] So there is a neutrino contribution (with H_(M+1) eigenvalueE_(v)) to the ambient physical wavefunction 2 from the M+1 thcosmological (huge!) source. Recall that the electron is itself the M thfractal scale source. So H_(M)→H_(e) gives eigenvalue E_(e). Note thatthe Ψ_(physical) must be finite inside the source (Mth fractal scale)but for t=∞ it appears infinite using equation 3 in equation 2 i.e.,Ψ_(physical) ∝ sin h(Ht/

)=sin h((Σ_(M)H_(M))∞/

). So the exponent of equation 2 must have in it:

Σ_(M) H _(M=)0  (6)

[0031] so that the sum of the Hamiltonians over all fractal scalesequals zero to make sure Ψ_(physical) is finite. So for exampleH_(M)+H_(M+1)=0 so that E_(e)+E_(v)=0 giving E_(v)=−E_(e). But for aneutrino with the same E_(v) that continues off into free spaceE_(M+1)ψ=E_(v) ψ=σ·ρ_(v) ψ∝γ⁵ ψ=helicityψ. So if E_(e) is positive thenE_(v) is negative (since E_(v)=−E_(e)) so the neutrino helicity isnegative (since it has the same sign as E_(v)) and so the neutrino isleft handed and (we have the negative sign in):

χ=½(1−γ5)ψ.  (7)

[0032] In decay we have the electron moving in the opposite directionand so to conserve angular momentum we have a lefthanded ψ (with N andN−1 th fractal scale) lefthanded doublet in decay

L _(fractal)=(i(ψ^(t))_(L)γμ({square root}{square root over (gμμ)}ψ,μ)_(L) +m(ψ^(t))_(L)ψ_(L) +{square root}{square root over (g_(N))} R_(N)+(L _(Source))_(N))  (8)

[0033] Thus we can write our lagangian over just one fractal scale(instead over an infinite number as in equation (1) by just including aleft handed zero mass component in ψ. This is our final lagrangian. Thisleft handed Dirac lagrangian doublet (with one constituent being nearzero mass) is at the core of the standard GSW electroweak model that hasitself been at the core of theoretical particle physics for the last 30years (Cottingham, 1998). The resulting single vertex Dirac S matrixgives the W and Z as resonances so it appears that the rest of thestandard model (such as φ⁴ potential and covariant derivativeconsequences) is implied by this model as well! But this model is moregeneral and so allows for the derivation of the standard modelparameters and lagrangian terms as a special case.

[0034] Propulsion

[0035] Equation 4 [that sin hωt, written out as X^(α)≡x^(α)-λ_(M) sinh(ω_(H)t), also from equation 1 we have Z_(oo)=8πe²/2mc²] implies thatto do the physics correctly we must do a radial coordinatetransformation to the coordinate system comoving with the cosmologicalexpansion giving: $\begin{matrix}{{\frac{\partial x^{0}}{\partial X^{\alpha}}\frac{\partial x^{0}}{\partial X^{\beta}}Z\quad \alpha \quad \beta} = {Z_{00}^{\prime} = {Z_{00} + z_{00}}}} & (9)\end{matrix}$

[0036] That z_(oo) turns out to be the classical gravitational source8πGρ and we can actually derive G here.

[0037] We can then create a ARTIFICIAL coordinate transformation usingchanging E&M fields that cancels the physical effects of the equation 9coordinate transformation that gave the gravity term z₀₀ in equation 9.In that case we could then cancel the effects of the gravitationalconstant G and so cancel out gravity and possibly inertia or even make Gnegative! This would certainly be an aid to propulsion technology. Soputting in the effects of a annulling C₀₀ into that coordinatetransformation X^(α)≡x^(α)-λ_(M) sin h(ω_(H)t) would modify thiscoordinate transformation to: $\begin{matrix}{{\frac{\partial x^{0}}{\partial X^{\alpha}}\frac{\partial x^{0}}{\partial X^{\beta}}{Z\quad}_{\alpha \quad \beta}} = {Z_{00}^{\prime} = {{Z_{00} + z_{00} - {C_{00}\quad {where}\quad C_{00}}} = {z_{00}.}}}} & (10)\end{matrix}$

[0038] So that X^(α)≡x^(α)-λ_(M) sin h(ω_(H)t)-λ_(M) sinh(ω_(H)t)=x^(α)+0. The zero signifies that our coordinate transformationeffect has been annulled and therefore there would be no gravitationalcontribution z_(oo) in equation 9. Thus our goal is to derive an E&Mconfiguration to artificially create this second

+λ_(M) sin h(ω_(M+1) t)≡C ₀ ≡C _(O)cancellation=term.  (11)

[0039] Thus the λ_(M) sin h(ω_(M+1)t) coordinate transformation term inequation (recall X^(α≡)x^(α)-λ_(M) sin h(ω_(H)t)) will cancel out andthe mass z_(oo) term then will be canceled out in equation thatcoordination transformation. To get the artificial equation 11cancellation term C^(o) we would like the most general (metric) E&Mphysical configuration available, which includes rotation. We then useit to derive X^(α)≡x^(α)−C^(α). The most general metric available to doall this is the Kerr metric (Hawking, 1973): $\begin{matrix}{{s^{2}} = {{\rho^{2}\left( {\frac{r^{2}}{\Delta} + {\theta^{2}}} \right)} + {\left( {r^{2} + a^{2}} \right)\sin^{2}\theta \quad {\varphi^{2}}} - {c^{2}{t^{2}}} + {\frac{2m\quad r}{\rho^{2}}\left( {{{asin}^{2}\theta \quad {\theta}} - {c{t}}} \right)^{2}}}} & (12)\end{matrix}$

 ρ²(r,θ)≡r ² +a ² cos²θ, Δ(r)≡r ²−2mr+a ²

[0040] We will derive equation 11 for the case of the Kerr metric. Forthat purpose we take the Kerr metric to be a quadratic equation in dt(∝C_(o)/c) and find from equation 1 (our using our new E&M source) theansatz$g_{00} \approx {1 - \frac{2\quad {{eV}\left( {x,\quad t} \right)}}{2m_{p}c^{2}}}$

[0041] from our new E&M source. We note that with the field magnitudeswe will have the solution: $\begin{matrix}{{dt} = {\frac{{- B} \pm \sqrt{B^{2} - {4{AC}}}}{2A} = {\frac{- B}{2A} \pm {\sqrt{\left( \frac{B}{2A} \right)^{2} - \frac{C}{A}}\left( {= {C_{o}\text{/}c}} \right)}}}} & (13)\end{matrix}$

[0042] so for smallest term (given the ± radical, note also 4AC=0 forA=0 and C is integrated over dt which is small relative to the dθ in the‘B’ term):${{cdt}\text{/}{dt}_{o}} = {{C\quad {^\circ}\text{/}{dt}_{o}} = {{{cB}\text{/}{Adt}_{o}} = {{2\quad {cc}\frac{4m}{r}\quad a\quad \sin^{2}{\theta d\theta}\text{/}{dt}^{o}\text{/}2A} = {annullement}}}}$

[0043] where A=c²−(2 m/r)c². With B carrying the angular momentum term.Notice though that if you varied 2 m/r just slightly around this valueof 1 you would radically change gravitational mass since this “A” iseverywhere in the denominator. m_(p)→m_(e) (electron mass) since here inmacroscopic applications the electron motion will dominate. So we make 2m/r=1 (then A will be nearly zero and so dt/dt_(o) very large)${\frac{4{mr}}{\rho^{2}} \approx \left( \frac{4e^{2}}{2m_{e}c^{2}r} \right)} = {2,\quad {\left( {{{- 4}{eV}/2m_{e}c^{2}} = {2V\text{/}512{kV}}} \right).}}$

[0044] Here we choose two counterrotating concentric cylinders. Recallfrom elementary physics that the electric potential V=ke/r=kQ/r for apoint source where in mks k=9×10⁹ Jm/C, e=1.6×10⁻¹⁹ C for a electroncharge, Q(=e) is the total charge. Or just use V=kQ/r for the potential,which you can measure with a voltmeter, which is the appropriatequantity to use for these experiments. So in g_(oo)=1-ke²/(mc²r) you canwrite g_(oo)=1-2 eV/2 mc². Now for that denominator “A” term: A=1-2ke²/2 mc²r=1-eV/mc² which equals zero for that singular case. Or (A=)1-e2V/2 mc²=0. So rearranging and using m=electron mass (=9.11×10⁻³¹kg), also c²=3×10⁸ squared=9×10¹⁶ m²/s²: so:V=mc²/e=9.11×10⁻³¹(9×10¹⁶)/1.6×10⁻¹⁹=512 kV. So that V(=ke/r)=2m_(e)c²/2 e=512 kV=V. Recalling that here V =512 kV leads to A=c²−(2m/r)c²≈0. So at 512 kV: $\begin{matrix}{{{Co}\text{/}{dto}} = {{{cB}\text{/}{Adto}} = {{2{cc}\frac{4m}{r}\quad a\quad \sin^{2}{\theta d\theta}\text{/}{dt}^{o}\text{/}2A} \approx {\pm \infty}}}} & (14)\end{matrix}$

[0045] depending on whether the (here tiny) “A” was positive ornegative. Since the electrons constitute so small a fraction of the massof the disc we see that for other charge on the disc not close to this512 kV value there will be little effect. Thus by just varying thevoltage above or below 512 kV you can make the disc containing thecharge extremely heavier or extremely lighter. But to go up the disc hasto be rotating rapidly so that the energy of rotation can be convertedinto potential energy to conserve energy: going up will mean adecreasing rotation rate of the disk for example. Thus essentially wecan make discs fly up rapidly and levitate just by varying the Voltageon the plate.

[0046] Note here for B/A to be nonzero in equation 14 we have a≠0 so theplates have to be rotating. g_(oo)=1-2 eV/2 mc² is singular at theradius r at which V=512 kV so the usual way “clocks” slow down andparticle positions remain stable (won't spark, holds together at surfacewhich is near 512 kV, so stays in ball. The means of propulsion here arecalibration of a prototype on the voltage of that negative dip inweight.

[0047] Prototype

[0048] We could build a prototype using the information gained from thisexperiment. Counterrotating discs (or free electrons at 512 kV movingrapidly between plates) will provide the propulsion. Energy istransferred from rotation to lift so that energy is conserved. Thevoltage at the lower weight spike (just above 512 kV) will be used forthis purpose. According to equation 14 you can control the up or downforce simply by controlling the voltage across rotating plates for whichthe voltage is just above 512 kV. Also the angular structure of thevalence electron cloud in the material must change with time by usingoscillating external fields for example. This is that dθ/dt in equation14 above provided by the microwave source.

[0049] Related Patents and other Confirmational Experimental Results

[0050] U.S. Pat. No. 593,138 is for a type of transformer that above 400kV (that voltage was recorded by later experimenters for this sameapparatus) creates an “electro-radiant” event (cloud of electrons) thatleaves perpendicular to the rotation direction of the current at above400 kV. There is a accompanying monodirectional repulsive impulse thatpenetrates all materials. The inventor apparently did a lot of researchverifying this result. Also U.S. Pat. No. 4,661,747 introduces a“conversion switching tube for inductive loads” that apparently createda similar pulse at a very high voltage. But note that our emphasis is ona static 512 kV rotator (with oscillation) that gives the mg lowering.This is not the same (pulse) concept as the previous two patents (butstill uses equation 14) which merely give additional evidence that thedevice we are patenting is viable. In addition here we propose theseresults as a theoretical explanation of a Russian experiment recentlycompleted and published Aug. 3, 2001 (Pod, 2001). Note that therotational dependence and mg spiking with voltage work was done prior toAugust 3. In the Russian experiment as the voltage went through ˜500 kV(in a type II SC) a positive and negative gravity pulse was created(recall the above diagram implies this also). The pulse was proportionalto the magnetic field put on the superconductor so that it wasproportional to the vortex velocity just as the above effect wasproportional to the capacitor rotational velocity. The above equation14, that gives these results, was presented in the February STAIF 2001(Maker, STAIF2001). These experimental results were presented in Aug. 3,2001. The gravity pulse was created by voltage on a superconductingdisc. An electron cloud in the form of a disk (instead of a spark! Onlysparks occurred below 500 kV) left the disc and moved rapidly to theanode in a low vacuum chamber. The gravity pulse itself left the chamberand was detected by pendulums (which moved) on the other side of theanode from the disk outside the chamber. The movement was independent ofthe mass of the pendulum implying that it was a “gravity” pulse.Unattenuated pulses (within measurement error) were detected at 100 mfrom the SC.

[0051] Angular Momentum and dt

[0052] Recall from just above equation 14 that A=c²[1-2 m/r] with 2m/r=2 e²/(2m_(e)c²r)=eV/(m_(e)c²)=V/512000, so also 4 m/r≈2 at 512 kV.Also in the classical Kerr solution a∝vr so angular momentum∝ma so areanormalized Angular momentum=a=(v/c)r. So equation 14 can be rewrittenas: $\begin{matrix}{= {\frac{c^{0}}{dt} = {{c^{2}\left( {2\frac{V}{512k}} \right)}\frac{\left( {v\text{/}c} \right)r\quad \sin^{2}{\theta d\theta}}{{dtc}^{2}\left\lbrack {1 - {V\text{/}512k}} \right\rbrack}}}} & (15)\end{matrix}$

[0053] The middle of the electron cloud is slightly closer to the anodeso it accelerates along the z axis at a slightly greater rate than theouter portion creating a bulge in the middle (so θ different on theoutside) that is directly proportional to the voltage traversed by thecloud. So the electron cloud is not flat when it reaches the anode, ithas a slight convexity or even ‘cusp’ to it. Lets say the voltagereaches its final value when θ is near 13° (or for the other material9.2°) so for the 13°=90°/convexity we have that convexity=7 and so inthat case polar angle θ=2π[V_(f)−V/7V_(f)] we have the changedθ=d2π(V_(f−V)/)7V_(f). Essentially you integrate from V=512 kV volts upto the final voltage v_(f). I assumed a disk that had a bumpheight/radius large enough to cause a corresponding uncertainty in thevoltage around that 512 kV value. So the “A” is not precisely zero andis displaced from zero by this small amount. I assumed that the upperpart of the vortex (in the 7×10⁻⁷ m) contained the contributing rotatingelectrons. Take the thickness of the SC disk to be 8 mm=T and the radiusto be 8 cm=r, the pulse rise dt=0.0001/2 sec (Pod,2001). I assumed thatthe electron velocity was the classical(e/m)rB=v=(1.6×10⁻¹⁹/9.11×10⁻³¹)(7×10⁻⁷)(0.9)=1.1×10⁵ m/s (not muchdifferent than the vortex velocity in the superconductor). So the radiusnormalized angular momentum is a=(v/c)r=(1.1×10⁵/3×10⁸)(0.08)=2.9×10⁻⁵

[0054] So equation 14 becomes: $\begin{matrix}\begin{matrix}{\frac{C^{o}}{dt} = {{c^{2}\frac{4m}{r}\frac{a\quad \sin^{2}{\theta d\theta}}{{dtc}^{2}\left( {1 - {2m\text{/}r}} \right)}} =}} \\{\frac{C^{o}}{dt} = {{c^{2}\left( {2\frac{V}{512k}} \right)}\frac{\left\lbrack {\left( \frac{v}{3{X10}^{8}} \right)r} \right\rbrack {\sin^{2}\left( {\frac{2\pi}{2*7}\frac{V_{f} - V}{V_{f}}} \right)}}{{dtc}^{2}\left( {1 - {V\text{/}512k}} \right)}\left( \frac{\pi}{2 \times 7} \right)\frac{dV}{V_{f}}}} \\{= {{c^{2}\left( {2\frac{V}{512k}} \right)}\frac{\left( {\left( {v\text{/}c} \right)r} \right){\cos^{2}\left( {\frac{\pi}{2 \times 7}\frac{V}{V_{f}}} \right)}}{{dtc}^{2}\left( {1 - {V\text{/}512k}} \right)}\frac{\pi}{2 \times 7}\frac{dV}{V_{f}}\left( \frac{2}{512k} \right){\frac{2.9 \times 10^{- 15} \times \pi}{{.\left( {{.0001}\text{/}2} \right)}V_{f}2*7}\left\lbrack \frac{V}{\left( {1 - {V\text{/}512k}} \right)} \right\rbrack}{\cos^{2}\left( {\frac{\pi}{2 \times 7}\frac{V}{V_{f}}} \right)}{dV}}} \\{\frac{C^{o}}{dt} = {5.14 \times {10^{- 7}\left\lbrack {\left( \frac{V}{V_{f}} \right)\frac{\cos^{2}\left( {\left( {\pi \text{/}2*7} \right)\left( {V\text{/}V_{f}} \right)} \right)}{1 - {V\text{/}512k}}} \right\rbrack}{dV}}}\end{matrix} & (16)\end{matrix}$

[0055] We next integrate this equation. Define $\begin{matrix}{{Integral} = {{5.14 \times 10^{- 7}{\int_{{512k} - \Delta}^{V_{f}}{\left( \frac{V}{V_{f}} \right)\frac{\cos^{2}\left( {\frac{\pi}{2*7}\frac{V}{V_{f}}} \right)}{\left( {1 - {V\text{/}512k}} \right)}\quad {V}}}} \equiv {Ve}}} & (17)\end{matrix}$

[0056] Close to the 512 kV singularity the V is not infinitely welldefined because of the SC surface irregularities. Also this integral wastaken numerically and Pod(2001) claimed that the pulse started at 500 kVinstead of 512 kV so we take Δ=12 kV. Thus for 500<V<512 we use the vevalue at 500 kV and for 520>V>512 ve has the value at 520 kV.

[0057] Comparison to Pendulum Tests

[0058] A pendulum in a evacuated chamber was placed on the lineconnecting the anode and the cathode but on the other side of the anodefrom the cathode. It was placed at various distances from the cathode. Arepulsive pendulum movement was observed that was independent of thetype of material or the mass the pendulum was constructed of. Thependulum displacement was measured (and so the final height) as afunction of the applied voltage V at the cathode. To help determine thenature of the voltage v we look toward the data presented in theaforementioned impulse experiments. Recall that ve is the voltageintegral to V_(f). in equation 17. So here the acceleration is given by$\begin{matrix}{{a(c)} \approx \frac{ve}{t}} & (18)\end{matrix}$

[0059] where again t is the impulse time given by Pod-Mod pulse risetime of t≈0.0001/2 sec. The velocity v applied to the pendulum mass bythe impulse is given by

ve={square root}{square root over (2gh)}  (19)

[0060] So that $\begin{matrix}{\frac{({ve})^{2}}{2g} = h} & (20)\end{matrix}$

[0061] This is the equation used to calculate the pendulum height as afunction of Voltage applied to the SC.

[0062] Putting the integral of equation 17 into equation 20 we get forindividual final heights (using a numerical integration fortran code) asa function of voltage and plotting the results together with theexperimental (Pod,2001):

[0063] Acceleration

[0064] Putting the integral of equation 17 into equation 18 (withimpulse rise time=t=0.0001/2 sec) we get the following (theoretical)pendulum accelerations (FIG. 3) at the given final voltages and cuspangles. Note the negative (attractive) spike near 500 kV, with above 512kV being positive (antigravity). So a smaller positive gravity impulseis seen and then the larger antigravity impulse at the higher voltages.Pod noted accelerations on the order of 1000 gs. Note also the pod(2001) microphone results (down and up dips in pressure) that can beinferred to be the results of the up and down spike results predictedabove.

[0065] References

[0066] Bjorken, Drell, Relativistic Quantum Mechanics, McGraw-Hill,(1964).

[0067] Cottingham W. N., An Introduction to the Standard Model ofParticle Physics, 1998, pp.112.

[0068] Feynman, R. P., Quantum Electrodynamics, Benjamin, N.Y., (1961).

[0069] Goldstein, Herbert, Classical Mechanics, 2nd Ed, Addison Welsey,1980 pp.576.

[0070] Graves, J. C,.Brill, D. R., “Oscillating Character of an IdealCharged Wormhole,” Phys.Rev 120 1507-17 , (1962).

[0071] Halzen F, A. D. Martin, Quarks and Leptons, Wiley, (1984).

[0072] Hawking, S, Large Scale Structure of Space-Time, CambridgeUniversity Press, (1973) pp.169.

[0073] Kursunglu B. N. and A. P. Wigner, Reminiscences about a GreatPhysicist: P.A.M. Dirac, Cambridge Univ. Press, Cambridge, (1987).

[0074] Liboff, Richard, Quantum Mechanics, 2nd ed., Addison-Wesley,(1991), pp.202.

[0075] Maker, David, Quantum Physics and Fractal Space Time, Chaos,Solitons, Fractals, Vol.10, No.1, (1999).

[0076] Maker, David, “Propulsion Implications of a New Source for theEinstein Equations,” in proceedings of Space Technology andInternational Forum (STAIF 2001), edited by M. El-Genk, AIP Proceeding552, AIP, NY, 2001, pp. 618-629.

[0077] Merzbachier, Quantum Mechanics, 2nd Edition, 1970 P.596,equations 24.21, 24.24.

[0078] Podlkletnov,(Pod) arXiv:physics/o108005, Aug 3, 2001.

[0079] Sokolnikof, Tensor Analysis, Wiley, (1964).

[0080] Weinberg,S., Relativity and Cosmology, Wiley, (1972).

1. We claim this invention provides a new form of electrostaticpropulsion and furthermore claim that there is adequate experimental andtheoretical evidence that it will work. The claim is that a rapidspherical rotator at just above 512 kV in a low amplitude oscillatoryelectric field will experience lower mg.
 2. A ramping up of the voltagethrough 512 kV will give an impulse out the back after the electroncloud from the cathode strikes an object such as anode. Also we claimthat there is adequate experimental and theoretical evidence that thiswill work. The theory behind claims 1 and 2 is the same.